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Math Help - "simple" math question

  1. #1
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    "simple" math question

    If cosA=cos B, then when does A=B? (Always, sometimes, never, infinite etc).

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  2. #2
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    No. Counterexample:

    \cos(0)=\cos(2\pi)=1 \Rightarrow 0 \neq 2\pi

    If you work on the interval \left[ 0, \pi \right], then \cos(a)=\cos(b)\Rightarrow a=b
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  3. #3
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    So what is the answer.. Never or sometimes?
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  4. #4
    Super Member bigwave's Avatar
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    it is always the same when it is a sign identity


    \cos\left({\theta}\right) = \cos\left({-\theta}\right)

    since \beta would just be a reflection of \alpha off the x axis then

    \cos{\alpha} = \cos{\beta}

    example:

    \cos\left({\frac{\pi}{4}}\right)<br />
 =\cos\left({-\frac{\pi}{4}}\right)<br />
 = \frac{\sqrt{2}}{2}
    Last edited by bigwave; February 4th 2010 at 12:10 PM. Reason: latex
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